(CNN) -- Schools in Memphis, Tennessee, will not open for the new school year until the school board receives at least $55 million of the money it is owed by the city.

The Memphis City Schools Board of Commissioners voted on the delay Tuesday night. However, Memphis Mayor A.C. Wharton Jr. told CNN Wednesday he is working toward a resolution, and "the children will not be caught in the middle."

The board vote indefinitely delayed school opening "pending the resolution of a long-standing funding dispute with the City of Memphis," school system attorney Dorsey Hopson said in a statement.

The board says it is owed a total of $151 million, according to the Commercial Appeal newspaper of Memphis. That includes what the city still owes for the 2008-09 school year, shortfalls on two subsequent school years and $78 million for the upcoming year.

The board wants $55 million immediately to open the schools, Martavius Jones, school board president, told CNN Wednesday. That "is the magic number," he said.

Board members passed a resolution asking that the remaining $23 million be paid after the city collects the funding in taxes, according to CNN affiliate WMC. Schools Superintendent Kriner Cash was directed last week to cut that $78 million from the current budget, WMC said.

Schools had been set to open August 8, with teachers due to report August 1.

"Someone has to assume responsibility for the collective education of the children in the city of Memphis, and I don't think the City Council can be exempt from that responsibility," board member Sara Lewis told WMC Tuesday night.

The school district sued the city in 2008 because of the funding dispute, Hopson said.

"The Shelby County Chancery Court and the State Appellate Court ruled that the city's decision to cut educational funding violated state law, and the state Supreme Court upheld the decision," Hopson said. "Despite these court rulings, the city has continuously failed to meet its legal obligation to adequately fund the district."

Since then, Jones said Wednesday, the board has relied on its savings. "We can no longer afford to do that," he said.

"For the last four years, the city of Memphis has withheld, illegally, funds that the State Supreme Court now has said is due our children," board member Kenneth Whalum Jr. told CNN Wednesday. Asked whether the measure isn't extreme, he said, "what's extreme is the fact that, even with a court order demanding the payment be made, that the city administrators would choose not to."

"I guess the political thing to do would be for me to say, 'Oh, they threatened us. They bluffed us. Let's just hold tight,'" Wharton said. But he said he has been speaking with council members and a school board member on Wednesday and is making progress. "Children shouldn't be caught in the middle," he said.

Jones cast the lone vote against postponing the beginning of the school year. He said Wednesday he is concerned the delay will mean students do not have enough time to prepare for standardized testing later in the fall.

"In order to deliver above and beyond service, we need the funding," he said. "We don't have enough money ... so the kids suffer."

"I'm all in support of us having assurances and money in the bank, but I think that 55 (million) was just an unreasonable amount to expect at this particular time and to postpone schools until we had that amount in the bank," Jones told reporters Tuesday night.

The dispute is worrisome to parents. "It's putting a lot of people under pressure," said parent Stephanie Addison-Jones. "But at the same time, the kids are first. Kids are our future."

Hopson said the school board had to make a tough decision.

"Although the decision will have a significant and adverse impact on students and families in Memphis, the board nevertheless concluded that it would be irresponsible to open schools, as planned, while cutting all non-mandated programs and service."

"The compromise is for the city to live up to its obligation and to see what it has not done in the past and make cuts on its end to pay for kids' education," Jones said.

The funding comes from property tax proceeds, Wharton told CNN, but "unfortunately, people do not pay their taxes on time, so we never have this huge pot of money at the beginning of school."

However, he said there is an agreement that would allow him to access funds the city is holding to settle an old lawsuit.

"We do not have $55 million, but we'll come up with something satisfactory to the Board of Commissioners or the school system, and satisfactory to the council and we'll get this done," the mayor said.

Asked whether the board would accept less, Whalum said he is not at liberty to agree to that, as the board resolution says $55 million.

"This is not just endemic to Memphis," he said. "It's a nationwide phenomenon, where local elected officials find other things to do with money that should be directed toward children."

Both sides met last Friday, Jones said, and city administrators agreed to pay $3 million of the $9 million it still owes for the 2010-11 school year. The funding was supposed to be delivered Monday, he said, but the board was still waiting Wednesday.

"They need to be in school," Cash told reporters Tuesday night, referring to students. "I can't say that passionately or emphatically enough, so I'm going to keep fighting to get a resolution to this matter with the parties that need to be involved, but we have to have it now. It's an urgent matter."